Stone Duality Type Theorems for MV-algebras with Internal State
Functional Analysis
2010-06-11 v1
Abstract
Recently in \cite{FM, FlMo}, the language of MV-algebras was extended by adding a unary operation, an internal operator, called also a state-operator. In \cite{DD1}, a stronger version of state MV-algebras, called state-morphism MV-algebras was given. In this paper, we present Stone Duality Theorems for (i) the category of Boolean algebras with a fixed state-operator and the category of compact Hausdorff topological spaces with a fixed idempotent continuous function, and for (ii) the category of weakly divisible -complete state-morphism MV-algebras and the category of Bauer simplices whose set of extreme points is basically disconnected and with a fixed idempotent continuous function.
Cite
@article{arxiv.1006.1960,
title = {Stone Duality Type Theorems for MV-algebras with Internal State},
author = {Antonio Di Nola and Anatolij Dvurecenskij and Ada Lettieri},
journal= {arXiv preprint arXiv:1006.1960},
year = {2010}
}